A play about a failed Middle East peace process in the early 1990s might not sound like a guaranteed theatrical hit. Plays about grand historical events and their disappointments can easily lapse into a never-ending scene of big names in smart suits meeting round big tables. David Hare’s Stuff Happens on Iraq captured the accident-prone nature of the undertaking but never wholly escaped the burden of the real action and suffering occurring offstage.

Yet Oslo, transferred to the National Theatre from the Lincoln Center, New York, and already nominated for the full shebang of multiple Tony awards, confounds such fears. It’s a moving, funny and insightful three hours, which (worry not) feel a lot shorter.

J.T. Rogers is a serious playwright with a gift for lightness, enhanced by Bartlett Sher’s direction. This account of the secret talks that led to the Oslo accords takes us from the first agreement made between the Palestine Liberation Organisation and Israel.

Crucially, it occurred behind the backs of the major powers, the brainchild of an academic and diplomat who were also husband and wife — Terje Rød-Larsen (Toby Stephens) and Mona Juul (Lydia Leonard), adding a wry domestic dimension (do you serve waffles to hardened Middle East bargainers?) to what might be bloodless roles.

It’s hard in a sombre global mood now to imagine how hopeful a moment the handshake between Yitzhak Rabin and Yasser Arafat was. The road to it is recaptured in all its ambition, nobility, quirks and setbacks.

The secret ingredient that makes Oslo feel so lively is its irreverence, even when the stakes are high and feelings and wounds run as deep as they do between Palestinians and Israelis. It bends verbatim theatre, crackling dialogue and high (and low) comedy, with a confident nod to Tom Stoppard’s ability to find the personal and sometimes absurd in grand politics. And like Stoppard’s Rosencrantz and Guildenstern Are Dead, it celebrates characters behind the scenes, rather than the big beasts. Henry Kissinger, for example, is portrayed in wicked impersonation by the Israeli intermediary.

Philip Arditti in this role is a lithe, sarky commentator on the uselessness of the rest of the world in dealing with his country’s complications. His Palestinian opposite number (Peter Polycarpou) is a prolix bon-vivant and Toby Stephens is the Norwegian PM, grasping his moment to break out of backwater politics and stick a polished shoe in the door of global affairs.